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In the Midpoint Rule for triple integrals we use a triple Riemann sum to approximate a...

In the Midpoint Rule for triple integrals we use a triple Riemann sum to approximate a triple integral over a box B, where

f(x, y, z)

is evaluated at the center

(xi, yj, zk)

of the box

Bijk.

Use the Midpoint Rule to estimate the value of the integral. Divide B into eight sub-boxes of equal size. (Round your answer to three decimal places.)

cos(xyz) dV, where B = {(x, y, z) | 0 ≤ x ≤ 2, 0 ≤ y ≤ 2, 0 ≤ z ≤ 2}
B
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